This paper presents a multi-compartment population balance model for wet granulation coupled with DEM (Discrete Element Method) simulations. Methodologies are developed to extract relevant data from the DEM simulations to inform the population balance model. First, compartmental residence times are calculated for the population balance model from DEM. Then, a suitable collision kernel is chosen for the population balance model based on particle-particle collision frequencies extracted from DEM. It is found that the population balance model is able to predict the trends exhibited by the experimental size and porosity distributions by utilising the information provided by the DEM simulations.

In this work we present a novel four-dimensional, stochastic population balance model for twin-screw granulation. The model uses a compartmental framework to reflect changes in mechanistic rates between different screw element geometries. This allows us to capture the evolution of the material along the barrel length. The predictive power of the model is assessed across a range of liquid-solid feed ratios through comparison with experimental particle size distributions. The model results show a qualitative agreement with experimental trends and a number of areas for model improvement are discussed. A sensitivity analysis is carried out to assess the effect of key operating variables and model parameters on the simulated product particle size distribution. The stochastic treatment of the model allows the particle description to be readily extended to track more complex particle properties and their transformations. product size/porosity distribution and Saleh et al. [17] investigated the effect of binder delivery method on the TSG system. Though the number of experimental investigations is extensive, the large operating window of TSG systems often limits the applicability of these results to local regions of the operating space.The comprehensive review of the experimental TSG literature by Seem et al. 50[18] shows a complex interplay between the role of each screw element type, the overall screw configuration, feed formulation and liquid flowrates on the observed experimental trends. This emphasises the need for a particle-scale model of TSG that can accurately predict the physical properties of the bulk granular 3 product. Ultimately, the inversion of such a model could then be carried out 55 and coupled with process control systems to allow specification and control of product specification in TSG systems.Granular systems are generally modelled using population balance models (PBM) [19,20,21,2, 22,23,24,25,26,27]. TSG specific PBMs have been developed, ranging from one [28] to three dimensional particle models [29,30]. 60A lumped parameter method is typically used to estimate additional particle properties beyond those explicitly tracked by the model [29]. Flow information and collision data have been incorporated into TSG models through couplings with alternative modelling frameworks such as the discrete element method (DEM) [29] and experimental near-infrared chemical tracing [31,28]. Many 65 of these TSG PBM studies have shown results in qualitative agreement with the experimental studies; however, quantitative predictions have proven to be much more challenging. One reason for this could be over-simplification of the system within the models. All of the existing TSG PBM models are numerically solved using variations of the sectional method [32]. Such a numerical approach 70

In this paper we present an experimental technique and a novel colourimetric image analysis algorithm to economically evaluate particle residence times within regions of batch granulators for use in compartmental population balance models. Residence times are extracted using a simple mixing model in conjunction with colourimetric data. The technique is applied to the mixing of wet coloured granules (binary and tertiary systems) in a laboratory scale mixer. The resulting particle concentration evolutions were in qualitative agreement with those from the mixing model. It was seen that the algorithm was most stable in the case of the binary colour experiments. Lastly, simulations using the Discrete Element Method (DEM) were also performed to further validate the experimental results. Particle concentrations from the simulations were in good agreement with the experimental results.

In this work, a framework for modelling twin-screw granulation processes with variable screw configurations using a high-dimensional stochastic population balance method is presented. A modular compartmental approach is presented and a method for estimating residence times for model compartments based on screw element geometry is introduced. The model includes particle mechanisms for nucleation, primary particle layering, coalescence, breakage, and consolidation. A new twin-screw breakage model is introduced, which takes into account the differing breakage dynamics between two types of screw element.Additionally, a new sub-model for the layering of primary particles onto larger agglomerates is presented. The resulting model is used to simulate a twin-screw system with a number of different screw configurations and the predictive power of the model is assessed through comparison with an existing experimental data set in the literature. For most of the screw configurations simulated, the model predicts the product particle size distribution at large particle sizes with a reasonable degree of accuracy. However, the model has a tendency to over-predict the amount of fines in the final product. Nevertheless, the model qualitatively captures the reduction in fines associated with an increase in the number of kneading elements, as observed experimentally. Based on model results, a number of key areas for future model development are identified and discussed. 35 may be quickly assessed without the usage of excipient/API or the need to set-up the device etc. This has generally been attempted through the use of compartmental population balance models (PBM) [12]. Several examples of compartmental twin-screw PBMs exist in the literature [13,14,15, 16,17]. In these examples, the screw barrel domain is modelled as a number of connected 40 compartments that permit process conditions and thus particle morphology to vary along the length of the simulation domain. These examples have used a sectional solution approach [18,19,20] which allows the compartmental PBM to be approximated and solved as a system of ordinary differential equations.This numerical approach generally limits the particle representation to taken 45 3 on three dimensions at most. The Stochastic particle method [21,22,23, 24,25,26,27,28] is alternative approach that has been employed to solve PBMs for batch granulation systems [29, 30,31,32,33,34,35,36, 37], silica [38] and TiO 2 [39] nano-particle synthesis, soot formation [40,41], and more recently twin-screw granulation [42, 43]. Unlike sectional methods, stochastic particle 50 methods permit much more complex particle representations, which can then be leveraged within the process model description, whilst still yielding a numerical problem that can be solved with acceptable levels of computational effort.The main aims of this paper are:1. Improve the stochastic TSG model in McGuire et al. [42, 43] based on the 55 areas identified for improvement. 2. Construct a modelling framework that allows for the compar...

In the second part of this study, we present the stochastic weighted particle population balance framework used to solve the twin-screw granulation model detailed in the first part of this study. Each stochastic jump process is presented in detail, including a new nucleation jump event capable of capturing the immersion nucleation processes in twin-screw granulation. A variable weighted inception algorithm is presented and demonstrated to reduce the computational cost of simulations by up to two orders of magnitude over traditional approaches. The relationship between the performance of the simulation algorithm and key numerical parameters within the nucleation jump process are explored and optimum are operating conditions identified. Finally, convergence studies on the complete simulation algorithm demonstrate that the algorithm is very robust against changes in the number of stochastic particles used, provided that the number of particles exceeds a minimum required for numerical stability.